Fundamental Study on Forecasting of Landslide Area(II)
On the time series of landslide frequency by the gamma distribution model and simulation
1981 Volume 33 Issue 3 Pages 8-17
Details
1981 Volume 33 Issue 3 Pages 8-17
The purpose of this study is to forecast the mean time of landslide occurring caused a heavy storm.The time series of landslide occurring ratio ηt was calculated by the next gamma distribution model.
ηt=F(C, rt)-F(C, rt-1)/F(C, rτ), F(C, rt)=1-∑e-1j=0(λr)j/j!e-λr
Function F is the probability that an unit slope will slide under the condition of resistance index C, shock rate λ and total precipitation at time t since a rain starts. Consequently F means the landslide area ratio of a watershed.
Monte Carlo simulation based upon the stated above model was carried out by an electro mini-computer according to the next procedure. The probability λΔrt was calculated following hourly precipitation Δrt. The judgment whether a shock would happen or not was decided at random by the next inequality,
ζt≤λΔrt :happen, ζtλΔrt :not happen
where ζt was a uniform random unmber ih the range(0, 1). These operation ware repeated through a series of hourly precipitation at a thousand unit slopes. Consequently an unit slope where many shock, for example j in above equation, were accumulated over the resistance index C was consider as the occurence of a landslide.
In this simulation, if the value C is small, the time series of landslide occurring ratio is influenced immeadiately by the pattern of hyetograph. Conversely if the value C is big, the response from rainfall to landslide occurring slows down and a single sharp peak appears behind the maximum hourly precipitation.
Meanwhile the time when landslides had broken out was searched by questioning and time series of landslide occurring ratio was got at Fujioka, Kuno and Minami Izu region.
At the results of the comparison with these series of landslides by questioning, calculation and simulation, the tendancy of these series are agree under the adequate resistance index C.
Therefore, the gamma distribution model and its simulation are effective significantly to forecast the mean time of landslide occurring at some arbitrary region. But the estimation on the resistance index C is difficult and controls the accuracy of a forecast.
